Abstract.
We present several constructions of a ``censored stable process'' in an open set D⊂R n, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time – we give sharp conditions for such approach in terms of the stability index α and the ``thickness'' of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent case. We also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary. We derive a boundary Harnack principle in C 1,1 open sets.
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Research partially supported by NSF Grant DMS-0071486.
Mathematics Subject Classification (2000): Primary 60G52, Secondary 60G17, 60J45
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Bogdan, K., Burdzy, K. & Chen, ZQ. Censored stable processes. Probab. Theory Relat. Fields 127, 89–152 (2003). https://doi.org/10.1007/s00440-003-0275-1
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DOI: https://doi.org/10.1007/s00440-003-0275-1